Answer:
[tex]\frac{x-2}{4x+5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4x^2+3x-1}{4x^2+9x+5}[/tex] ÷ [tex]\frac{4x^2+7x-2}{x^2-4}[/tex]
Factorise numerator / denominator of both fractions
= [tex]\frac{(4x-1)(x+1)}{(4x+5)(x+1)}[/tex] ÷ [tex]\frac{(4x-1)(x+2)}{(x-2)(x+2)}[/tex]
Cancel common factors on numerator/ denominator of both fractions
= [tex]\frac{4x-1}{4x+5}[/tex] ÷ [tex]\frac{4x-1}{x-2}[/tex]
Change ÷ to × and turn second fraction upside down
= [tex]\frac{4x-1}{4x+5}[/tex] × [tex]\frac{x-2}{4x-1}[/tex]
Cancel the common factor 4x - 1 on numerator/ denominator, leaving
[tex]\frac{x-2}{4x+5}[/tex]
